Smoothed dissipative particle dynamics - a mesoscopic particle-based hydrodynamic technique for complex fluids

Smoothed dissipative particle dynamics (SDPD) combines two popular mesoscopic techniques, the smoothed particle hydrodynamics and dissipative particle dynamics (DPD) methods, and can be considered as an improved DPD approach. Advantages of the SDPD method over conventional DPD include the possibility of using an arbitrary equation of state, direct input of transport properties, and a well-defined physical scale of discretized elements or fluid particles. The SDPD method has been already applied to a number of mesoscopic problems involving complex fluids. Despite several advantages of the SDPD method over the conventional DPD model, the original formulation of SDPD by Español and Revenga (2003) lacks angular momentum conservation, leading to unphysical results for problems where the conservation of angular momentum is essential. To overcome this limitation, the SDPD method is extended by introducing a particle spin variable such that local and global angular momentum conservation is restored. The new SDPD formulation (SDPD+a) is directly derived from the Navier-Stokes equation for fluids with spin, while thermal fluctuations are incorporated similar to the DPD method. In this chapter, we describe the basics of the SDPD method and show several of its applications including particle margination in blood flow. In addition, the SDPD method with angular momentum conservation is validated using two problems: (i) the Taylor-Couette flow with two immiscible fluids and (ii) a tank-treading vesicle in shear flow with a viscosity contrast between inner and outer fluids. For both problems, the new SDPD method leads to simulation predictions in agreement with the corresponding analytical theories, while the original SDPD method fails to capture properly physical characteristics of the systems due to violation of angular momentum conservation.